Solve the equation
-$2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$
A) 16
B) -2,-1
C) 2,- $\frac { 1 } { 2 }$
D) 16,$\frac { 1 } { 16 }$

Question

Solve the equation
-$2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$
A) 16
B)  -2,-1 
C)  2,- $\frac { 1 } { 2 }$
D)  16,$\frac { 1 } { 16 }$

Quizplus · Accepted Answer

Squaring both sides of the equation gives $4x-12x^{1/2}+9x^{1/4}-4=0$. Letting $u=x^{1/4}$, we get $4u^4-12u^2+9u-4=0$. Factoring gives $(u-1)(4u^3+4u^2-5u+4)=0$. Solving $u-1=0$ gives $u=1$, so $x^{1/4}=1$ and $x=1$. Solving $4u^3+4u^2-5u+4=0$ gives $u=\frac{1}{4}$, so $x^{1/4}=\frac{1}{4}$ and $x=\frac{1}{16}$.

Solve the Equation - 2x1/2−3x1/4−2=02 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 02x1/2−3x1/4−2=0

Solve the Equation
- $2 x ^ { 1 / 2 } - 3 x ^ { 1 / 4 } - 2 = 0$